(Very minor spoiler) There is a moment in which people are waiting for something, and then we see one of the machines walking towards them from the horizon, and there's just this very powerful sense of impending doom.
I like end of the world type movies that make you think "Wow, this could be it!" as opposed to Independence Day goofy stuff like giving computer viruses to alien technology.
I have never seen Independence Day. (Probably the only person on the planet who can say that!) My favorite sci-fi are the real old black and white movies. Them! is one of the best of that genre. I also like the hokey ones where you can see the zipper on the creature's costume. :o) They're the best!